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A232883
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Decimal expansion of Sum_{i>=0} (1/(2*i^2+1)).
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3
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1, 6, 3, 7, 1, 6, 0, 2, 6, 7, 1, 1, 7, 9, 6, 7, 2, 4, 6, 4, 3, 7, 2, 6, 4, 4, 9, 5, 8, 0, 0, 5, 7, 3, 5, 7, 3, 9, 3, 7, 2, 6, 3, 3, 6, 8, 4, 5, 0, 6, 9, 4, 6, 1, 9, 2, 6, 2, 2, 8, 2, 4, 1, 9, 9, 2, 6, 6, 6, 9, 0, 2, 9, 7, 0, 6, 0, 9, 1, 1, 2, 5, 8, 2, 4, 3, 3, 0
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OFFSET
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1,2
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LINKS
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FORMULA
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Equals 1/2 + ( Pi/sqrt(2) ) /tanh( Pi/sqrt(2) ) /2.
Equals 1 + Sum_{k>=1} (-1)^(k+1)*zeta(2*k)/2^k. - Amiram Eldar, Jun 17 2023
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EXAMPLE
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1.6371602671179672464372644958005735739372633684506946192622824199...
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MATHEMATICA
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RealDigits[1/2 + Pi/Sqrt[2]/Tanh[Pi/Sqrt[2]]/2, 10, 90][[1]]
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PROG
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CROSSREFS
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Cf. A072691 (Sum_{i>=1} (1/(2*i^2))), A113319 (Sum_{i>=0} (1/(i^2+1))).
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KEYWORD
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AUTHOR
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STATUS
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approved
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